R Statistics Cookbook

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Putting a specific value for the Bernoulli variables can be viewed as putting a random variable with all its probability mass at 0.5. We could do something slightly more elaborate without making such a strong compromise on the specific value.

Instead of using a fixed value for the Bernoulli variables (0.5), we can use a ka parameter and then put a prior on ka. For example, we can use a beta distribution that is bounded between 0 and 1 (and can be used to generate priors for probabilities, such as our q parameter for a Bernoulli variable). Let's use beta (5,5) random variable. What this means is that, instead of saying that we think with a 100% probability that the proportion of irrelevant variables is 0.5, we are now splitting ...